Tentang NPV and IRR calculator (with MIRR and payback)
NPV discounts each period's cash flow back to the start and adds them up: NPV = Σ CF_t ÷ (1 + r)^t, with the first flow at period 0. IRR is the discount rate at which NPV is exactly zero. MIRR instead assumes outflows are funded at a finance rate and inflows reinvested at a reinvestment rate. Payback counts the periods until cumulative cash turns positive, and discounted payback does the same with present values.
With the defaults, an outlay of 10,000 followed by 3,000, 4,200 and 6,800, discounted at 10%, the NPV is 1,307.29 and the IRR is 16.34%. The money comes back after 2.41 periods, or 2.74 periods counting the time value of money. MIRR, at a 10% finance rate and 12% reinvestment rate, is 15.15%.
A period can be a year, a quarter or a month, as long as the rate is for the same period. Flows that change sign more than once can have several IRRs; the result then warns you and MIRR is the better guide.
Pertanyaan
How do you calculate NPV?
Divide each cash flow by (1 + r)^t, where t is its period, and add the results, counting the initial outlay at t = 0. At 10%, the flows −10,000, 3,000, 4,200 and 6,800 are worth −10,000 + 2,727.27 + 3,471.07 + 5,108.94 = 1,307.29. A positive NPV means the project earns more than the discount rate.
Why does Excel's NPV function give a different answer?
Excel's NPV treats the first value in its range as arriving at the end of period 1, not at period 0. Putting all four default flows into =NPV(10%, …) returns 1,188.44, which is 1,307.29 ÷ 1.1. To get the usual NPV, leave the initial outlay out of the function and add it separately: =NPV(10%, 3000, 4200, 6800) − 10000.
How is IRR calculated?
IRR is the rate that makes NPV zero, and it has to be found by trial: there is no general formula beyond four periods. For the default flows it is 16.34%. Excel's IRR starts from a 10% guess and returns #NUM! if it has not converged after 20 tries; here the search scans rates from −99.9% to 1,000% and then refines the root.
What is the difference between IRR and MIRR?
IRR implicitly assumes every inflow is reinvested at the IRR itself; MIRR uses a stated reinvestment rate and finance rate, and it always has a single answer. In Microsoft's example, −120,000 followed by 39,000, 30,000, 21,000, 37,000 and 46,000 has an IRR of 13.07% but an MIRR of 12.61% at a 10% finance rate and 12% reinvestment rate.
What is the difference between payback and discounted payback?
Payback counts plain cash; discounted payback counts present values, so it is always longer when the rate is positive. For the default flows, cumulative cash is −2,800 after two periods and the third period's 6,800 covers it in 0.41 of a period, a payback of 2.41. At 10% the discounted payback is 2.74 periods. Neither measure counts cash after the payback point.
Seberapa akurat “NPV and IRR calculator (with MIRR and payback)”?
Akurasi bergantung pada masukan dan asumsi metode. Aritmetika desimal memakai 50 digit signifikan, tetapi perkiraan, metode numerik dan data sumber bisa kurang presisi; pembulatan yang ditampilkan tidak menghilangkan batasan itu. Contoh penyelesaian yang diperiksa dengan sumber independen: 6. Misalnya, “Four-year project at 10%” diperiksa dengan Python decimal (prec 50) script: textbook NPV, IRR by 300-step bisection, Excel MIRR definition. Microsoft's NPV example gives 1,188.44 for these flows with the first at t = 1; ×1.1 = 1,307.28.
Dari mana metode ini berasal?
Microsoft Excel IRR function; Microsoft Excel MIRR function; Microsoft Excel NPV function; Brealey, Myers & Allen — Principles of Corporate Finance, ch. 5 (NPV and other investment criteria).